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Theorem 2eu5 2288
 Description: An alternate definition of double existential uniqueness (see 2eu4 2287). A mistake sometimes made in the literature is to use to mean "exactly one and exactly one ." (For example, see Proposition 7.53 of [TakeutiZaring] p. 53.) It turns out that this is actually a weaker assertion, as can be seen by expanding out the formal definitions. This theorem shows that the erroneous definition can be repaired by conjoining as an additional condition. The correct definition apparently has never been published. ( means "exists at most one.") (Contributed by NM, 26-Oct-2003.)
Assertion
Ref Expression
2eu5
Distinct variable groups:   ,,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem 2eu5
StepHypRef Expression
1 2eu1 2284 . . 3
21pm5.32ri 619 . 2
3 eumo 2244 . . . . 5
43adantl 452 . . . 4
5 2moex 2275 . . . 4
64, 5syl 15 . . 3
76pm4.71i 613 . 2
8 2eu4 2287 . 2
92, 7, 83bitr2i 264 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wex 1541  weu 2204  wmo 2205 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209 This theorem is referenced by:  2reu5lem3  3043
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